Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\sqrt{2}}{\frac{1 + t}{\sqrt{2}}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]
1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
1 - \frac{1}{2 + \left(2 - \frac{\sqrt{2}}{\frac{1 + t}{\sqrt{2}}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}
double f(double t) {
        double r923203 = 1.0;
        double r923204 = 2.0;
        double r923205 = t;
        double r923206 = r923204 / r923205;
        double r923207 = r923203 / r923205;
        double r923208 = r923203 + r923207;
        double r923209 = r923206 / r923208;
        double r923210 = r923204 - r923209;
        double r923211 = r923210 * r923210;
        double r923212 = r923204 + r923211;
        double r923213 = r923203 / r923212;
        double r923214 = r923203 - r923213;
        return r923214;
}
↓
double f(double t) {
        double r923215 = 1.0;
        double r923216 = 2.0;
        double r923217 = sqrt(r923216);
        double r923218 = t;
        double r923219 = r923215 + r923218;
        double r923220 = r923219 / r923217;
        double r923221 = r923217 / r923220;
        double r923222 = r923216 - r923221;
        double r923223 = r923216 / r923219;
        double r923224 = r923216 - r923223;
        double r923225 = r923222 * r923224;
        double r923226 = r923216 + r923225;
        double r923227 = r923215 / r923226;
        double r923228 = r923215 - r923227;
        return r923228;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \frac{\color{blue}{\sqrt{2} \cdot \sqrt{2}}}{1 + t}\right)}\]

  5. Applied associate-/l*0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + t}\right) \cdot \left(2 - \color{blue}{\frac{\sqrt{2}}{\frac{1 + t}{\sqrt{2}}}}\right)}\]

  6. Final simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{\sqrt{2}}{\frac{1 + t}{\sqrt{2}}}\right) \cdot \left(2 - \frac{2}{1 + t}\right)}\]

Reproduce

herbie shell --seed 2019143 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))